Which equation can be used to solve for 
\[x\] in the following diagram?
Two lines intersecting each other, are creating opposite angles of 60 degrees and x+45 degrees.
\[60^\circ\]
\[(x+45)^\circ\]
Choose 1 answer:
Choose 1 answer:
(Choice A)   
\[60 + (x + 45) = 90\]
A
\[60 + (x + 45) = 90\]
(Choice B)   
\[60 + (x + 45) = 180\]
B
\[60 + (x + 45) = 180\]
(Choice C)   
\[(x + 45) = 90 - 60\]
C
\[(x + 45) = 90 - 60\]
(Choice D)   
\[60 = (x + 45)\]
D
\[60 = (x + 45)\]

In this problem, the two angles given are opposite (vertical) angles formed by the intersection of two lines. Vertical angles are always equal.

Given:
- One angle is \(60^\circ\).
- The other angle is \((x + 45)^\circ\).

Since vertical angles are equal, we can set the two angles equal to each other:

\[
60^\circ = (x + 45)^\circ
\]

So, the correct equation to solve for \(x\) is:

**Choice D:** \(\boxed{60 = (x + 45)}\)

Would you like to know how to solve for \(x\) using this equation? Here are 5 related questions you might find interesting:

1. How do you solve the equation \(60 = x + 45\) for \(x\)?
2. What are vertical angles, and why are they equal?
3. How would the equation change if the angles were complementary instead of vertical?
4. What would the equation be if the given angle were \((x + 45)^\circ\) and the opposite angle were \(75^\circ\)?
5. How can you verify your solution for \(x\) once it's found?

**Tip:** When dealing with angles formed by intersecting lines, always check if they are vertical or adjacent to use the appropriate property (e.g., vertical angles are equal, adjacent angles sum to \(180^\circ\)).

Learn how to solve for x in a geometric problem involving angles formed by intersecting lines. Understand the concept of vertical angles and how they are used to solve equations. Suitable for high school students studying geometry.

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